Well....a frog fell into a hole that was 14 ½ feet deep. He could jump 3 feet, but he slid back a foot each time he jumped. How many jumps does it take him to get out of the hole?

Question

anonymous · Answer

Each jump we advance three feet $+3$ but slide back a foot $-1$ so each jump gives us a net advancement of $+2$. For an integer number $n$ jumps, we have $+2n$ and we want $+2n\ge14\frac12$. Dividing both sides by two gives us $n\ge 7\frac14$ hence the minimum whole number of jumps needed is $8$.